# Thread: What values f(X) can get ?

1. ## What values f(X) can get ?

Hi Guys,

I try to calculate the values that this function can "get".

According to my calcs, it's X<=-4 or X>4.
When I plotted it, I saw that it also gets values between -3 and 2. I don't understand why. Can anyone please show me the calculations that bring to that result ?

cheers !

2. $f(x) = \dfrac{\sqrt{x^2 + 2x - 8}}{\sqrt{x^2 - x - 12}} = \dfrac{\sqrt{(x+4)(x-2)}}{\sqrt{(x+3)(x-4)}}$

So, x cannot be equal to -3 or 4, because there, you have an asymptote.
At x = -4 and 2, you have f(x) = 0.

Anything negative is imaginary.

When you take the intervals, you have -4, -3, 2, 4.

And trying in values smaller than -4 gives a solution.
At -4, you have 0.
Between -4 and -3, you don't have any solution.
At -3, you get infinity.
Between -3 and 2, you get solutions.
At 2, you get 0 again.
Between 2 and 4 you get no solutions.
At 4, you get again infinity and beyond that, you get solutions.